吴消元法在线性系统解耦问题中的应用.pdf

th Proceedings of the 25 Chinese Control Conference 7-11 August, 2006, Harbin, Heilongjiang 吴消元法在线性系统解耦问题中的应用 1,2 1 冯俊娥 ，徐胜元 1. 南京理工大学自动化系, 南京 210094 E-mail: fengjune@sdu.edu.cn 2. 山东大学数学与系统科学学院, 济南 250100 摘 要: 利用吴消元法讨论了线性系统的输入-输出全解耦问题, 包括线性奇异系统和线性时滞系统等情形. 输入- 输出全解耦问题即输入-输出传递函数的非奇异对角化问题是一类多项式方程组的求解问题, 对于多项式方程组 求解问题, 吴方法给出了一套机械化算法. 本文利用吴消元法讨论了线性系统多种反馈情形下的解耦问题, 给出 了问题可解的充要条件, 并且举例说明本文方法的正确性, 同时与已有文献中的例子加以比较. 关键词: 吴消元法, 输入-输出解耦, 线性系统 INPUT-OUTPUT DECOUPLING OF LINEAR SYSTEMS VIA WU ELIMINATION METHOD Feng Jun-e1,2, Xu Shengyuan1 1. Department of Automation, Nanjing University of Science and Technology, Nanjing, 210094 E-mail: fengjune@sdu.edu.cn 2. School of Mathematics and System Science, Shandong University, Jinan 250100, China Abstract: The paper discussed the problem for input-output decoupling of linear systems via wu elimination method, including the cases of linear singular systems and linear time-delay systems. The problem of input-output complete decoupling is that of diagonalization nonsingular transfer function which can be transformed into solving problem of multipolynomial equations. Based on algebraic geometry, the Wu method provides a mechanical algorithm for solving the problem of input-output complete decoupling via several feedback cases. Necessary and sufficient conditions for decoupling problems were given. Several examples were presented, and some of them were compared with ones of other papers. Key Words: Wu Elimination, Input-output